Question: Simplify the following expression: $t = \dfrac{-24r - 108}{120r + 12}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-24r - 108 = - (2\cdot2\cdot2\cdot3 \cdot r) - (2\cdot2\cdot3\cdot3\cdot3)$ The denominator can be factored: $120r + 12 = (2\cdot2\cdot2\cdot3\cdot5 \cdot r) + (2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $t = \dfrac{(12)(-2r - 9)}{(12)(10r + 1)}$ Dividing both the numerator and denominator by $12$ gives: $t = \dfrac{-2r - 9}{10r + 1}$